2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79621The spectral properties of the Ruelle transfer operator which arises from a given polynomial wavelet filter are related to the convergence question for the cascade algorithm for approximation of the corresponding wavelet scaling function.AMS-LaTeX; 38 pages, 10 figures comprising 42 EPS diagrams; some diagrams are bitmapped at 75 dots per inch; for full-resolution bitmaps see ftp://ftp.math.uiowa.edu/pub/jorgen/convcasc/Functional Analysis46L60, 47D25, 42A16, 43A65 (Primary) 46L45, 42A65, 41A15 (Secondary)Convergence of the cascade algorithm at irregular scaling functionstext